inductive reasoning get ready to think need to use all of your background knowledge
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Inductive Reasoning Get Ready to Think!!! Need to use all of your background knowledge!. 1.7. Inductive Reasoning. To make conclusions based on patterns you observe. Example: The past 3 three days have been sunny so it should be sunny tomorrow. Conjecture.

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inductive reasoning
Inductive Reasoning
  • To make conclusions based on patterns you observe.

Example:

The past 3 three days have been sunny so it should be sunny tomorrow.

conjecture
Conjecture
  • The conclusion to your inductive reasoning

Example:

It will be sunny tomorrow

ellipses
Ellipses

Three dots after a pattern that indicates the pattern continues

look for patterns
Look for Patterns

Examples: Write a rule for the pattern and find the next two numbers.

1.) 30, 25, 20, 15,…

Start with 30 and subtract 5 repeatedly; 10,5

2.) 2, -2, 2, -2…

Alternate 2 and its opposite; 2,-2

3.) 1, 3, 4, 12, 13,…

Start with 1 alternate multiplying by 3 and adding 1;39,40

4.) 3, 9, 27, 81,…

Start with 3 and multiply by 3 repeatedly; 243, 729

5.) 1, 1, 2, 3, 5, 8,…

Add the previous two numbers together; 13, 21

predictions
Predictions

Your conjecture is a prediction and it may be true or false.

counterexample
Counterexample
  • One example that proves the statement to be false.
  • You only need one to prove the conjecture is not correct
determine if the conjecture is correct or not if it is incorrect give a counterexample
Determine if the conjecture is correct or not. If it is incorrect, give a counterexample

6.) The last digit of the product of 5 and a whole number is either 0 or 5.

correct

7.)A number and its absolute value are always opposites.

False; 2 and the absolute value of 2 are not opposites. (you could pick any positive number as a counter example.) This only holds true for negative numbers

homework
Homework

TB: Pg 38 (1-23) odd

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